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Many physical systems that have interacting structures that span wide ranges in size involve substantial scale invariant (or scaling) subranges. In these regimes, the large and small scales are related by an operation that involves only the scale ratio. The system has no intrinsic characteristic size. In the atmosphere gravity causes differential… (More)

This paper shows how modern ideas of scaling can be used to model topography with various morphologies and also to accurately characterize topography over wide ranges of scales. Our argument is divided in two parts. We first survey the main topographic models and show that they are based on convolutions of basic structures (singular-ities) with noises.… (More)

The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian 1 noises. However, there are both theoretical and empirical reasons to consider similar equations driven by strongly non-Gaussian noises. In particular, they yield strongly non-Gaussian anomalous diffusion which seems to be… (More)

Starting about thirty years ago, new ideas in non-linear dynamics, particularly fractals and scaling, provoked an explosive growth of research both in modeling and in experimentally characterizing geosystems over wide ranges of scale. In this review we focus on scaling advances in solid earth geophysics including the topography. To reduce the review to… (More)

We demonstrate that the Fokker-Planck equation can be generalized into a 'Fractional Fokker-Planck' equation, i.e. an equation which includes fractional space differentiations, in order to encompass the wide class of anomalous diffusions due to a Lévy stable stochastic forcing. A precise determination of this equation is obtained by substituting a Lévy… (More)

[1] Climate sensitivity (l) is usually defined as a deter-ministic quantity relating climate forcings and responses. While this may be appropriate for evaluating the outputs of (deterministic) GCM's it is problematic for estimating sensitivities from empirical data. We introduce a stochastic definition where it is only a statistical link between the forcing… (More)

Lindborg et al. (2010) claim that the apparent spectrum power law E(k) ≈ k −3 on scales ≥ 600 km obtained with the help of commercial jetliner trajectory deviations (GASP and Mozaic databases) could not be brought into question (Lovejoy et al., 2009a), because this spectrum corresponds to " a well known theory of quasi-geostrophic turbulence developed by… (More)

After having closely reexamined the notion of a Lévy's stable vector, it is shown that the notion of a stable multivariate distribution is more general than previously defined. Indeed, a more intrinsic vector definition is obtained with the help of non isotropic dilations and a related notion of generalized scale. In this framework, the components of a… (More)